Topological reach of field-theoretical topological quantum computation
Topological Data Analysis A software surveycv.mikael.johanssons.org/talks/2013-09-eccs.pdf ·...
Transcript of Topological Data Analysis A software surveycv.mikael.johanssons.org/talks/2013-09-eccs.pdf ·...
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Topological Data AnalysisA software survey
Mikael Vejdemo-JohanssonComputer Vision and Active Perception Laboratory
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Cubical homologyPixels and voxels
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Cubical homologyPixels and voxels
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Cubical homologyPixels and voxels
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Cubical homologyPixels and voxels
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ChomP
• Cubical homology — with or without persistence
• GUI, command line interface, and C++ library
• Encodes a wide range of both space and mapping analyses
• Includes a wide range of homotopy-based optimizations
http://chomp.rutgers.edu/Software.html
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HAP
•Module for the GAP computer algebra system
• Primarily focused on research programming into group cohomology
• Includes support for cubical persistent homology
http://www.gap-system.org/Packages/hap.html
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Persistent (co)homologyPoint cloud topology
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Persistent (co)homologyPoint cloud topology
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Persistent (co)homologyPoint cloud topology
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Persistent (co)homologyPoint cloud topology
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Persistent (co)homologyPoint cloud topology
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1-dimensional features barcode
Persistent (co)homologyPoint cloud topology
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Plex / jPlex / javaPlex
• Family of software packages developed at Stanford, adapted for use from Matlab
• Implements a range of algorithms — both for constructing complexes and computing their persistent (co)homology
• Current recommended incarnation: javaPlexhttp://javaplex.googlecode.com
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Dionysus
• Library for computational homology
• Contains example applications implementing persistent homology and cohomology, as well as time-varying persistence (vineyards) & low-dimensional optimizations
• Relies on Boost, and optionally on CGAL for low-dimensional optimizations
• Includes a Python interface through Boost::Python
http://www.mrzv.org/software/dionysusWednesday, March 19, 14
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pHat
• Recent released software package and C++ library
• Implements several optimizations to the persistence algorithm
• Does not (currently) construct the complex for you
• (currently) restricted to ℤ2 coefficients
• Some support for SMP parallelization using OpenMP
http://phat.googlecode.comWednesday, March 19, 14
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Perseus
• Cubical and simplicial complex representation and several different construction methods
• Uses discrete morse theory to speed up computation
http://www.math.rutgers.edu/~vidit/perseus
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ToMaTo
• C++ library for topological analysis
• Relies on libANN for approximate nearest neighbors
http://geometrica.saclay.inria.fr/data/ToMATo/
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GAP Persistence
• Persistent homology and complex construction in the GAP computer algebra system
http://www-circa.mcs.st-and.ac.uk/~mik/persistence/
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Mapper
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Mapper
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Mapper
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Mapper
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Mapper
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Ayasdi / Iris
• Proprietary software package for Mapper-based topological data analysis
• Very intuitive graph display interaction UI
• Statistical tests and factor identification built-in
http://www.ayasdi.com
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Python Mapper
•Open source solution
• Developed by Müllner & Babu at Stanford University
• Focused on being a research tool
• Exports graph structure in several formats: GraphViz .dotd3.js JSON graph representation
http://math.stanford.com/~muellner/mapper
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Thank you for listening;now go forth and experiment
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